I am still trying to wrap my mind around why bigger AB amps often times have better bass, even though the output may be the same as a class A amp.
What is most likely happening here is that the fully Class A amps require so much constant DC that the power supply just doesn't have enough on tap for the powerful bass hits. It requires an enormous amount of power supply capacitance to supply enough "smooth DC" power for that constant 30 watt Class A sink -- that it's only just enough to carry through for normal music. When bass frequencies hit, it will pull even more on the power supply, which is just treading water enough to keep the voltage up (though I suspect voltage will dip anyways on the high power bass hits). I suppose the exception would be very huge amp, such as the XA200 monoblocks, or something like a Krell FPB300+ monoblocks.
On a large Class AB amp, such as X250.8, the power supply is sized larger than the XA30 with a larger transformer as well so that it can sustain that 250 watts per channel. However, you hardly use much of that, probably 5-10 watts constant draw during normal music and when the bass hits, the power supply transformer and capacitance has enough current on tap to push that bass frequency waveform through the speaker before it needs to draw on the main A/C current to recharge the power supply caps. The power supply is able to draw A/C voltage at 60 hz, which is generally fast enough to keep the power supply full for low bass frequencies.